Sure, I would almost certainly be dead, but life on Earth would continue, our species would continue, and our civilisation would continue (albeit with some major setbacks).
Besides, I don't think anyone's nuclear war plan is actually to destroy every major to semi-major city on Earth. In a realistic 1980s nuclear war, a lot of nukes would be targeted at military bases and the like. Plenty of others would destroy every major city in the US and USSR, plus each country's nuclear-armed allies. Maybe we here in Australia would get a nuke or two out of spite. But is anyone going to bother to nuke South America?